Peter Lindqvist

Notes on the Stationary p-Laplace Equation (eBook, PDF)

• Format: PDF

Produktbeschreibung

>2) or singular (p<2). Thus it requires advanced methods. Many fascinating properties of the Laplace equation are, in some modified version, extended to the p-Laplace equation. Nowadays the theory is almost complete, although some challenging problems remain open.

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Produktdetails

• Verlag: Springer Nature Switzerland
• Seitenzahl: 104
• Erscheinungstermin: 26. April 2019
• Englisch
• ISBN-13: 9783030145019
• Artikelnr.: 56831327

Autorenporträt

Peter Lindqvist is Professor of Mathematics in the Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim, Norway. His research focus is analysis, including in particular partial differential equations and "non-linear potential theory".

Inhaltsangabe

1 Introduction.- 2 The Dirichlet problem and weak solutions.- 3 Regularity theory.- 4 Differentiability.- 5 On p-superharmonic functions.- 6 Perron's method.- 7 Some remarks in the complex plane.- 8 The infinity Laplacian.- 9 Viscosity solutions.- 10 Asymptotic mean values.- 11 Some open problems.- 12 Inequalities for vectors.

Rezensionen

"The book will provide the reader with an up-to-date overview on the p-Laplace equation and will uncover ideas behind some concepts and involved results in the field." (Vladimir Bobkov, Mathematical Reviews, December, 2019)
"The book is a very useful contribution to the growing literature on this circle of ideas. I wholeheartedly recommend this book both as a textbook, as well as for independent study." (Vicentiu D. Radulescu, zbMATH 1421.35002, 2019)